In a recent publication, we presented a new strategy for engineering design and optimization, which we termed formulation space exploration. The formulation space for an optimization problem is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into this new space, the solution to any optimization problem is no longer predefined by the optimization problem formulation. This method allows a designer to both diverge the design space during conceptual design and converge onto a solution as more information about the design objectives and constraints becomes available. Additionally, we introduced a new way to formulate multiobjective optimization problems, allowing the designer to change and update design objectives, constraints, and variables in a simple, fluid manner that promotes exploration. In this paper, we investigate three use scenarios where formulation space exploration can be utilized in the early stages of design when it is possible to make the greatest contributions to development projects. Specifically, we look at s-Pareto frontier generation in the formulation space, formulation space boundary exploration, and a new way to perform inverse optimization. The benefits of these methods are illustrated with the conceptual design of an impact driver.

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